Triple correlations of Fourier coefficients of cusp forms

2016/07/11 by Yongxiao Lin, Lin, Yongxiao
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1607.02956

openalex publication_date 2016/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We treat an unbalanced shifted convolution sum of Fourier coefficients of cusp forms. As a consequence, we obtain an upper bound for correlation of three Hecke eigenvalues of holomorphic cusp forms ∑_{H≤ h≤ 2H}W((h)/(H))∑_{X≤ n≤ 2X}λ₁(n-h)λ₂(n)λ₃(n+h), which is nontrivial provided that H≥ X^2/3+ε. The result can be viewed as a cuspidal analogue of a recent result of Blomer on triple correlations of divisor functions.

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